If the staid monuments to British war heroes in London’s Trafalgar Square could talk, they might order the kid on the rocking horse to settle down. Powerless Structures, Fig. 101, on display on the square’s Fourth Plinth until summer, depicts a carefree child at play. Shirtless, wearing suspenders and waving his arm with abandon, the three-ton bronze figure makes the nearby equestrian statue of George IV (wittily referenced in the hobbyhorse) look positively dour. The boy’s insouciance, his creators say, also takes a dig at the British tradition of building monuments to commemorate military victories.

“We basically want to say there is something else to celebrate,” says Ingar Dragset, sitting in a low-slung leather chair in his Berlin studio. Michael Elmgreen, his long-time collaborator, is more explicit. “The London mayor’s office kindly asked us not to describe it as an antiwar sculpture,” he says of the piece. “But it is.”

For nearly 20 years, Elmgreen, a 51-year-old Dane, and Dragset, a 43-year-old Norwegian, have said whatever they want, regardless of the controversy it may generate. Frequently cheeky and often irreverent, their defiant art probes the status quo and inevitably finds it wanting. In a work called Gay Marriage, they dismissed the dangers associated with same-sex unions by uniting two porcelain urinals with a single hose. In Prada Marfa, they parodied the exclusivity of luxury brands by placing a replica of a Prada boutique—replete with handbags and shoes but lacking a door—in the middle of a Texas desert. And last fall they installed a giant bed featuring an ominous vulture perched on one of its posts inside the Louis Vuitton flagship store in London. Titled One Night Awaits Us All, the piece hinted that everyone—from wealthy patrons to shop clerks—meets the same fate. It also challenged the store’s rather genteel employees to break protocol in favor of an occasional nap. They did. “Every time we do a work,” Elmgreen says, “it’s a question of, What would happen if?”

Throughout 2013 the duo will pose that question often in their role as honorary curators for the city of Munich. Hoping to dust off the well-to-do Bavarian city’s fusty image and draw tourists back from Germany’s reigning capital of cool, Berlin, officials handed Elmgreen and Dragset more than $1.5 million to stage “A Space Called Public.” Running until September, the project will include up to a dozen works by international artists that question how the city shapes its identity. “Munich’s machinery runs so well that officials are bored by themselves,” Dragset says. “They’ve asked us to throw some dirt at them.”

Among the grit are Berliner Pfütze (Berlin Puddle), an installation by Kirsten Pieroth that will regurgitate rainwater from Berlin onto the streets of Munich for one month, and Malaysian-born Han Chong’s Made in Dresden, a giant Buddha, buttocks exposed, that will recline in Viktualienmarkt, the city’s open-air marketplace. Elmgreen and Dragset will also contribute two works of their own. In one, which previously ran in Rotterdam, a performer will remove a stainless-steel megaphone from a glass cabinet once an hour and shout, “It’s never too late to say you’re sorry!”

“It not only reminds people who pass by that they should apologize to their mom or girlfriend, but it also offers catharsis,” Elmgreen says. The performance will take place on the Odeonsplatz, where Hitler delivered some of his most notorious speeches.

In October the duo’s curatorial prowess goes on show again at London’s Victoria & Albert Museum. To create Tomorrow, they will convert five rooms into a fictitious architect’s home stocked with furniture (including the bed from Louis Vuitton) and works they have sourced from their personal collections. A written handout will tell the story of the architect’s failed ambitions, turning the space into a metaphor for his frustration. “In their work, people are the uninvited visitors,” Louise Shannon, the curator overseeing the V&A exhibition, says of the pair. “They use objects to weave spectacular narratives around things that may seem completely mundane.”

The artists’ personal narrative began in Copenhagen at a gay bar called After Dark, where they met in 1995. They went home together only to discover that they already lived in the same apartment building. Elmgreen, a poet turned artist, introduced Dragset, then a mime fresh out of theater school, to Copenhagen’s contemporary art scene. In an early work, they knitted skirts and slowly unraveled them off each other in public spaces, including a locker room and a public toilet. “It was like an unspectacular peep show that took a long time,” Dragset says, noting that their main goal was simply to spend time together. “We were using inexpensive materials that went against gay identity, which was considered more flashy and clichéd.”

Disillusioned by their respective home countries, which they still view as monocultural and unsupportive of outsiders, they moved to freewheeling Berlin in 1997. Dragset, who grew up in a close-knit family, eventually emerged as a father figure for the older Elmgreen, who had run away at 16 and never saw his parents again. “I don’t respect authority, but I needed someone to be close to,” Elmgreen says. “I have a tendency of not being very steady.”

The couple bristled at what they saw as attempts to categorize them as a gay double-act specializing in lighter works and soon dreamed up bigger sculptural pieces in response. In an early sculpture, they installed the base of a diving board inside Denmark’s Louisiana Museum of Modern Art, with the board poking out the window toward the sea, suggesting that museums should connect more with the real world. Then came the mammoth Dug Down Gallery, located in a field outside Reykjavík, Iceland, which reimagined the bare white interior of a contemporary art gallery as a massive, roofless hole in the ground. Later, in a daylong performance piece called The Great Escape, they mocked the art world’s haughtiness and self-importance by having workers pack up the entire collection of a Düsseldorf art museum. They then drove it around the block one time and reinstalled each item in its original location.

A growing international profile and a steady stream of commissions spoke to the success of their professional collaboration, but 10 years after meeting, their personal relationship had waned. “If you want to keep things fresh, you need to mess them up,” Elmgreen, the more loquacious of the two, says. “You need to be on thin ice, and you need to experience new things. Splitting up was part of that.” The tense transition led to some disturbing works. Just a Single Wrong Move, part of a show at London’s Tate Modern, consisted of a highly realistic animatronic sparrow that twitched and writhed on a windowsill in apparent pain. Its placement behind glass meant no one could come to its aid.

Today Elmgreen lives in London, though he visits Dragset several times a year in Berlin, where they have a studio, a former pumping station, that spans five floors and has 42-ft. ceilings on the ground level.

Their work process is one of collaboration but not compromise: assisted by a full-time staff of six, each sees a project through on his own from beginning to end, and they resolve differences of opinion by pursuing entirely new paths rather than accommodating with trade-offs. When apart, they speak on the phone up to 10 times a day and communicate regularly by e-mail. “I would never do art without Ingar,” Elmgreen says. “Our chemistry and the excitement of creating together is what drives it all.”

Although they choose to live outside Scandinavia, both artists prize the values upon which the region’s welfare states were built. A pair of upcoming works assert their shared belief that society should look after the well-being of the poor and vulnerable. In the fall they’ll reveal a permanent installation in a ritzy new business district of Oslo, where they will clad a decrepit, 90-ft. chimney in bronze and stainless-steel rings to resemble a stack of gigantic—and completely useless—Norwegian coins. Called Change, it’s a reminder of values beyond money. And later in the year they’ll unveil The Weight of One Self outside the Palais de Justice in Lyon, France. The marble figure—a man carrying a drowned version of himself—takes another swipe at society’s failure to help those in need.

What takes place once their work appears in public has a tendency to surprise even them. Short Cut, a car and trailer that appeared to burst through the floor of Milan’s Galleria Vittorio Emanuele II, became a favorite site for newlyweds to pose for photos. Fashionistas still make pilgrimages to Prada Marfa to leave offerings of rocks and shoes or, like Beyoncé, to photograph themselves dancing in front of it. And Dug Down Gallery turned into an after-hours party venue. “When you put art out there,” Elmgreen says, “it has a dangerous life, but also a more real life.”

Aside from the playful interactions their work encourages, much of the artists’ appeal stems from a knack for reimagining the familiar. Just as Duchamp famously drew a mustache on the Mona Lisa, they’re not afraid to appropriate existing objects to make a point. Located in Berlin’s Tiergarten, their Memorial for the Homosexual Victims of the Nazi Regime alludes to the city’s Memorial to the Murdered Jews of Europe, which consists of a series of grey concrete stelae. “We make the stela ours,” Dragset says. “It’s a queer-looking one leaning to the side.” Last June, they unveiled Han, a reinterpretation of Denmark’s beloved Little Mermaid statue, at the end of a dock in Elsinore. Han—Danish for “him”—depicts a naked man who assumes the original mermaid’s languorous pose on an identically shaped rock. Critics roared that the homoerotic statue had no place in a former shipyard where strong men once worked. But the artists say Han better reflects the man on the street than do classical statues that appear to be on steroids.

This same irreverence extends even to their own mounting fame. Last year the Queen of Denmark presented the duo with the Eckersberg Medal, one of the country’s most prestigious awards. Elmgreen, who missed the ceremony because of a bout with the flu, keeps his bronze medallion in a sock drawer and plans to melt it down and turn it into a work for a show at Denmark’s National Gallery in 2014. “It’s good to get medals because you can use them for something,” he says. “It’s disrespectful, but disrespectful isn’t bad.”